Regularizations and quantum dynamics in loop quantum cosmology

TL;DR

This paper analyzes different regularization prescriptions in loop quantum cosmology, focusing on the Yang-Ding-Ma approach, and introduces a semiclassical method to evaluate quantum trajectories, revealing how choices affect quantum dynamics.

Contribution

It provides a detailed mathematical and dynamical analysis of the Yang-Ding-Ma regularization in LQC and develops a robust semiclassical method for evaluating quantum trajectories.

Findings

Yang-Ding-Ma prescription's quantum dynamics confirmed and extended.

A semiclassical method for analytical quantum trajectories is devised.

Evaluation of trajectories across prescriptions demonstrates method robustness.

Abstract

One of critical components of Loop Quantum Gravity (LQG) and Cosmology (LQC) -- Thiemann regularization procedure is non-unique. Different choices of particular prescriptions lead to models which differ in both mathematical structure and physical predictions. Here we briefly recall a set of such prescriptions proposed in the literature in context of isotropic LQC on the example of a flat universe with massless scalar matter content. For the one least investigated so far, further called Yang-Ding-Ma prescription, a detailed analysis of its mathematical structure and resulting quantum dynamics is performed, confirming and extending the results obtained so far by phenomenological methods. In order to probe the dynamics, a relatively robust method (working in the approximation of the macroscopic universe) of evaluating quantum trajectories is devised. Said method is a variant of a semiclassical treatment that allows to express the trajectories analytically as function of internal clock and a set of certain central moments -- constants of motion encoding quantum corrections up to arbitrary order in systematic manner. As a test of method's robustness analogous evaluation of the quantum trajectory in volume is performed for those of other prescriptions, for which it is applicable. The limitations of the treatment are further briefly discussed.